The 21-year-old full back's deal expires at Griffin Park in June and he has impressed in recent cameos.
It was Clarke's cross that led to Scott Hogan's equaliser against Bristol City and he produced an excellent display against Cardiff on Tuesday.
Smith said: “Josh has been one that's ongoing since I've been here. I needed to have a good look at him.
“He's come back and impressed me in training, enough to put him on the pitch as a sub and start him on Tuesday night. The information I'd pass on to the directors of football would be a positive one.”
Smith believes a decision has yet to be made about Marco Djuricin, although GetWestLondon understands the Bees are unlikely to make his loan deal permanent.
He said: “I was aware of what Marco had done before I came. I spoke with Lee Carsley about him and what he offered.
“He was injured when I came and Lasse was on fire. It hasn't happened for him unfortunately.
“He came on against Walsall and missed a couple of chances. It's not happening for him in front of goal. He needs to be working hard and it'll come.”
In the development squad, Jan Holldack has caught the fans' eye with his performances but it appears a role in the first team is unlikely at this current time.
Smith explained: “He's another in the development squad who has done really well. He was playing centre back and playing as a midfielder.
“We're trying to find his best position before I bring him into the first-team squad.”